Nah, that’s not it. I drove for both in a major city in the months before the virus and outside of peak hours Lyft always has substantially longer pickup times. This is based on a few hundred rides for each company. This means that they have fewer passenger per driver, so the biggest delta is a smaller user base. Once the lockdown began Lyft rides basically evaporated overnight, while Uber was still going strong at certain times and certain places, catering to essential workers. But both are worthless as a way to make money right now.
I believe Lyft generally has a slightly wealthier clientele: more middle-class people choosing not to drive. Uber has more reach in the lower ends of the market. So when the stay-at-home orders flooded in, these middle-class people all stayed at home, while Uber was still serving essential workers.